Skat

Skat is the national card game of Germany and has an international association that maintains the rules and organises tournaments across Germany and Europe. It is best played with 3 players, but there is variant for two players that is good for learning.

Skat is another sub-culture you had no idea existed. Here below is some play from a Skat championship from 2014.

• Skat is played with 32 cards – the cards of the standard 52 card deck from A to 7 inclusive
• There are 3 players and each player gets 10 cards in the deal, and two are placed to one side and are known as the Skat.
• The game uses the cards in an Ace-Ten ordering: the Ace is high, the next highest card is then the 10, then the King, the Queen, but not the Jack. Jacks are special
• Jacks are always trump cards and are higher than the Aces, and Jacks have an order amongst themselves: the Jack of Clubs is higher than the Jack of Spades, which is, in turn, higher than the Jack of Hearts, which is higher than the Jack of Diamonds
• When a suit is designated as the Trump suit, all the Jacks belong to the Trump suit and are higher in value than the Ace of the trump suit. If a player leads a Jack, other players must play a trump and the trumps include all the other Jacks.
• Unless you play a no-Trump game, in which case, the Jacks form a fifth suit all off their own. You can Trump with a Jack if you have no cards of the suit played. If a player leads a Jack, you must also play a Jack, or slough.

I should add that I am interested in the structures of games because I design protocols for allocating resources. It is useful to analyse how games are structured so that one can devise strategies. If you play Texas Hold’em, you may know that the best strategy is to play “Tight and Hard”. Skat is a very sophisticated game and there are a lot of strategies.

Here is a strategy for playing the Trump suit. If you have played Whist, or Bridge, you’ll know that if you have a long suit, you would choose to make that the Trump suit. If you then lead with trump cards, you will be able to eliminate all of the trump cards in your opponents hand and you will have the remaining trumps which are then the highest cards and will win.

Now in Whist, there are 52 cards, with four suits of 13 cards, so you would have dominant long suit if you have 7 or more cards in one suit. In a 4 player game, 13 cards of a suit would usually be spread evenly with each player having more or less 3 cards or each suit. A dominant suit is 7 of one suit.

Skat has 32 cards, 8 of each suit and only three players, so usually each player gets 3 of each suit. But the Trump suit becomes 12 cards when the Jacks join it, so having the dominant suit is easier to achieve.

Because of this, Skat is more decisive than Whist. By decisive, I mean that there are:
either fewer outcomes or some outcomes are much more likely than others.

Skat like most sophisticated games uses an auction to contract one player to an outcome. Each player’s understanding of his hand is translated into a series of bids – the bid is the expected earnings from the hands the players hodl. The players then compete in the bidding. The player winning the auction makes a contract based on his bid, the other two players than cooperate to cause the winning player to fail.

The bidding is the most complicated part of the game. Before I get onto to that, I will just explain how a game is decided.

Unlike Whist, a player wins when they have collected 61 points or more in the trick-taking part of the game. When a player wins a trick with the highest card, he collects those cards and they contribute to his trick-taking score. The cards have the following values: Ace is 11, the Ten is 10, the King is 4, the Queen 3, the Jacks are only 2 and all the other cards have no point value. 9, 8 and 7 are all valued at 0. Totals are 44, 40, 16, 12, 8 and 0 so 120 points to win. And, of course, 60 points is half of the points total of all ten tricks, so 61 is half the points plus 1 point.

If the player wins at least 61 points, he also needs the Game-Value to exceed his bid. The Game-Value is not calculated from the trick-taking points, but rather from the structure of the hand played. The structure of the hand played depends on which suit was designated as the Trump suit and how strong the winning bidder’s hand is.

The suits have been given base values. The suits are ranked in the same order as the Jacks: Clubs, Spades, Heart and Diamonds and the base values are respectively 12, 11, 10, 9.

So, if a player were to make a bid of 9, he would be expected to declare diamonds as trumps. If he then went on to make 61 points in the trick-taking part of the game, he would be awarded +9 points. If he fails to make 61 points, he is penalized -18 points, that is double.

Skat then introduces a confusing concept to judge how strong the player’s hand is. If he holds all 4 Jacks, his hand is considered very strong, and is described as “with 4 and plays as 5”. The Game-Value for trumps as diamonds is then 45 which “plays as 5” multiplying the base value of 9.

So the Game-Value is the base value of the trump suit multiplied by (1 + 4). Where the “1” is given the bidder for winning the bid, but the “4” is given to him for holding all four Jacks.

The evaluation of the multiplier for a player is very esoteric. The “with” of “with 4” actually means you have the top-rated Jack, the Jack of Clubs. If you only hold the Jack of Clubs, you would be “with 1 plays as 2”, and you would multiply the base suit by (1 + 1) or for diamonds you would have a Game-Value of 18. If you do not have the Jack of Clubs, but hold any other Jack, you are “without 1 plays as 2” and the same calculation for 18.

It gets more involved. If you have the top two black Jacks, you are “with two plays 3”, if you have the bottom two red Jacks, you are “without two plays 3”. If you have the top three Jacks, you are “with 3 plays 4”; if you have only the bottom Jack, of Diamonds, you are “without 3 plays 4”.

It might be apparent that the “with” and “without” statements are in fact duals. The first example was all four Jacks and was “with 4 plays as 5”, if you have no Jacks, you are “without 4 and plays as 5”.

It gets more involved, the Jacks have to form a sequence from the Jack of Clubs, so if you hold the Jack of Clubs, but not the Jack of Spades, and you also hold the bottom two red Jacks, you are still “with 1 plays 2”.

And there’s a further twist, if you have all 4 Jacks and you also hold the Ace of some suit, then were you to declare that suit as Trump, then you would be “with 5 play 6”. Because the multiplier is designed to evaluate how you strong your Trump suit is an you have the top 5 trump cards. If you had the 10 of that Trump suit you are “with 6 play 7” and so on for the King and the Queen of that suit – resulting in “with 8 plays as 9”.

You might have noticed that all hands – will be “with” or “without” something.

There are other multipliers too. Remember the Skat? The two cards that were put to one side. The player winning the bid can elect, after bidding, to take those two cards into his hand and discard two. Usually, one would choose to do this to further strengthen one’s hand, but one may choose not to do so in which case, one declares “Hand” and can add another 1 to the multiplier, so one might be actually say “with 1 plays as 2 with Hand plays as 3”.

If the winning bidder goes on to make 91 points, then he is has “Schneider” and can add another 1 to his multiplier. Further, if he declares before playing that he can make “Schneider” he adds another 1 to his multiplier and then receives one, if he achieves it. If he has announced “Schneider” but fails to achieve it, the announcement multiplier is still counted in the penalty score.

And finally there is Schwarz, if the bidding player wins all the tricks, he gets Schneider and the Schwarz and so adds two to his multiplier, and he can also choose to announce Schwarz and receive another two, giving him in total 4 to add to his multiplier. If he announces Schwarz but fails to make it, he is penalized for the whole 4 and fails the contract.